Global optimization requires global information

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There are many global optimization algorithms which do not use global information. We broaden previous results, showing limitations on such algorithms, even if allowed
to run forever. We show deterministic algorithms must sample a dense set to find the
global optimum value and can never be guaranteed to converge only to global optimizers.
Further, analogous results show introducing a stochastic element does not overcome these
limitations. An example is simulated annealing in practice. Our results show there are
functions for which the probability of success is arbitrarily small.